Performance Improvement of Voronoi Constellations by Multi-Dimensional Rotation for Fading Channels

High transmission quality is essential for wireless communication. To meet this demand, we propose an approach to enhance the modulation method using Voronoi constellations (VCs) based on an N-dimensional lattice partition. Compared to traditional methods such as Mary phase-shift keying ( M-PSK) and M-ary quadrature amplitude modulation (M-QAM) on a two-dimensional plane, w-dimensional VCs offer a larger Euclidean distance between signal points, resulting in superior error rate performance in additive white Gaussian noise (AWGN) channels. To further improve performance in fading channels, we introduce new VCs that achieve diversity gain by rotating the constellation in W-dimensional space while preserving AWGN channel characteristics. Numerical results demonstrate that VCs achieve a 25 dB gain for QPSK and a 17 dB gain for 16QAM at a block error rate of 10−4 in a symbol-independent and identically distributed (i.i.d.) Rayleigh fading channel. Additionally, as the achieved diversity gain is influenced by fading variations, the effective range of these gains was clarified in accordance with the 5G New Radio (NR) radio interface.